After you explore Route 5 and go through the Underground Path, you reach Route 6.
Explore the Route
In the grass in this area, you can find Jigglypuff, Psyduck, Vulpix, Rattata, Pidgey, Pidgeotto, and others.
If you go north from the exit from the Underground Path, you will see an entrance to a guard house. Don't go inside (the guard inside won't let you go north), but go to the right of the guard house entrance and check the ground to find a hidden Rare Candy.
To the left of the guard house entrance, there is a Super Potion.
South of the guard house, you can battle Picnicker Nancy, who has a level 15 Nidoran♀ and a level 15 Jigglypuff. You get 300 Pokédollars and 2 Great Balls for winning.
To the left of Nancy, you can battle Camper Ricky, who has a level 15 Sandshrew and a level 15 Nidoran♂. You get 300 Pokédollars and 2 Great Balls for winning.
To west of the Camper and Picnicker, you can battle Gentleman Edward, who has a level 16 Eevee. You get 1920 Pokédollars and 3 Poké Balls for winning.
To the left of the Gentleman, there is a Guard Spec.
Go east from there, then south, and you can battle Sailor Elijah, who has a level 16 Tentacool. You get 960 Pokédollars and 3 Poké Balls for winning.
Go south, then west until you find a Paralyze Heal.
Then go south, and you can battle Picnicker Isabelle, who has a level 15 Charmander. You get 300 Pokédollars and 2 Great Balls for winning.
To the right of Isabelle, you can battle Camper Jeff, who has a level 15 Bellsprout. You get 300 Pokédollars and 2 Great Balls for winning.
Go south and you will arrive in Vermilion City.